Calorimetric study of small clusters and single magnetic ions in dilute(Sr, Eu)S

The specific heat of insulating $\left({\mathrm{Sr}}_{1-x}{\mathrm{Eu}}_x\right)\mathrm{S}$ with $0.017<~x<~0.07$ was measured between 0.04 and 2 K. The magnetic specific heat $C_M$ consists of two contributions: a roughly constant term $C_M^P$ between 0.3 and 1.2 K, which can be explained as arising from exchange coupled ${\mathrm{Eu}}^{2+}$ pairs and small clusters. At lower temperatures where $C_M^P$ drops exponentially to zero, the contribution from the remaining isolated ${\mathrm{Eu}}^{2+}$ spins becomes important. The freezing of these single spins at ≃ 0.01 K gives rise to a $T^{-2\mathrm{}}$ term of $C_M$.